A triangle has corners at $(6, 5)$ $(6 ,5 )$ , $(1, - 6)$ $(1 ,-6 )$ , and $(- 2, 9)$ $(-2 ,9 )$ . If the triangle is dilated by a factor of $5$ $5$ about point #(5 ,-5 ), how far will its centroid move?

Question

1367 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-02-10T08:03:11

Centroid moves by $\approx 33.44$ $~~ color(green)(33.44)$ due to dilation factor of 5 about point $((5),(-5))$

Centroid $G( ((6+1-2)/3),((5-6+9)/3)) = ((5/3),(8/3))$

Dilated about $((5),(-5))$ by a factor of 5

New coordinates of centroid G'

$vec(G'D( = 5 * vec(GD)$

((x-5),(y+5)) -> 5((5/3 - 5),(8/3+5)) = ((50/3),(115/3))#

$G'((x),(y)) = ((15),(100/3))$

Distance between G & G'

$vec(GG') = sqrt((15-5/3)^2 + (100/3-8/3)^2) ~~ color(green)(33.44)$

A triangle has corners at (6 ,5 )(6,5)(6 ,5 ), (1 ,-6 )(1,−6)(1 ,-6 ), and (-2 ,9 )(−2,9)(-2 ,9 ). If the triangle is dilated by a factor of 5 55 about point #(5 ,-5 ), how far will its centroid move?